Maximum likelihood estimation of earthquake hazard parameters in the Aegean area from mixed data

Tectonophysics, 185 (1991) 277-294

Elsevier Science Publishers B.V., Amsterdam

277

Maximum likelihood estimation of earthquake hazard parameters in the Aegean area from mixed data

Gerassimos A. Papadopoulos a*b~l and Andrzej Kijko ’

a Department of Civil Engineering. Hellenic Air Force Academy, Dekelia, Attika, Greece

b Department of Natural Disasters, Ministry of Environment, Physical Planning and Public Works,

2 Panormou Str., 11523 Athens, Greece

’ Institute of Geophysics, Polish Academy of Sciences, fiiecia Janusza 64, 01-452 Warsaw, Poland

(Received February 25,199O; revised version accepted May 29,199O)

ABSTRACT

Papadopoulos, G.A. and Kijko, A., 1991. Maximum likelihood estimation of earthquake hazard parameters in the Aegean area from mixed data. Tectonophysics, 185: 277-294.

The maximum likelihood estimation of earthquake hazard parameters has been made in the Aegean and adjacent regions

on the basis of a procedure which utilizes mixed data containing incomplete files of large historical events, and complete files

of most recent earthquakes. The entire earthquake catalog used covers the period from 479 B.C. to 1985 A.D. The maximum

regional magnitude, M,,,,, the activity rate of the seismic events, the mean return period, R, of earthquakes with a certain

lower magnitude M> m, as well as the parameter b of the magnitude-frequency relationship have been determined for

eighteen different seismotectonic segments, the fore-arc and back-arc regions, and the area examined as an entity. The

determination has also been carried out for sub-crustal shocks in the south Aegean. Assuming that the earthquake hazard is an

increasing function of M,,,, and a decreasing function of R, we suggested a relative hazard scale to classify segments by

hazard level based on their M_ and R. It is shown that in general the hazard is higher in the back-arc segments than in the

fore-arc ones. High differences of the b parameter and the hazard level from segment to segment reflect the high seismotectonic complexity and crustal heterogeneity.

Introduction

The term “natural hazard” refers to a poten- tially damaging or destructive natural event such

as an earthquake, volcanic eruption, tsunami etc.

Here the term “seismic hazard” is used to describe

earthquake size measured by surface-wave magni-

tude, M.

Seismic hazard studies in the Aegean region

have been published by several authors cited in

the relevant works of B&h (1983a, b) and Malcro-

poulos and Burton (1985). The seismic activity in

this region is extremely high and much has oc-

curred within the historical period. One would,

’ Address for correspondence: 98 Mavromichali Str., 11472 In this paper we use this approach to estimate

Athens, Greece. seismic hazard parameters in several seismo-

therefore, expect a considerable amount of seismo-

logical information to be available. However, the

incompleteness of the data, even for earthquakes

of large magnitude, make the existing historical

catalogs unsuitable for use in seismic hazard

evaluation based on most methods proposed. Nev-

ertheless, Kijko and Sellevoll (1987; 1989) have

developed an approach utilizing the information

on strong events contained in the macroseismic

part of catalog as well as that contained in the

complete catalog. Hereafter we use “subcatalog”

to refer to any part of the catalog which contains

complete data above a certain magnitude

threshold. The part of catalog covered by the

subcatalogs is called the “complete part” while the

remaining is the “extreme part” of the catalog.

oo40-1951/91/$03.50 0 1991 - Elsevier Science Publishers B.V.

278

tectonic segments of the Aegean and adjacent regions. Such a study is of importance for two main reasons:

(1) We evaluate hazard parameters utilizing as much as possible seismological ~fo~ation not only from the instrumental period, i.e., the time during which measurements were made but also the many hundreds of years previous to this of the historic era. In other words, we use historical seismological information not used so far in Aegean hazard determination.

(2) Tbe application of that approach in a region with high seismotectonic complexity and high seismicity is a good methodological test offering a suitable basis for seismotectonic discussions.

Theory and notation

b = slope of the Gutenberg-Richter (G-R) magnitude-frequency relation

P = parameter interrelated to b (b =

8 log el x = activity rate of the seismic events

x0 = value of X corresponding to mO

m0 =~~rnurn(rn~); i=l,...,s

“I = magnitude threshold in the i-th complete subcatalog

.s = number of complete subcatalogs M *ax = maximum possible magnitude in the

specified region m = a certain earthquake magnitude R = return period of earthquakes with mag-

nitude M 2 m T = time period covered by the whole cata-

log; (T, + T,)

T, = time interval covered by the extreme part of the catalog

T, = time interval covered by the complete part of the catalog

77 = time length of the i-th complete subcatalog; i = 1,. . . , s

n = total number of earthquakes

a, = number of events in the extreme part of the catalog with magnitudes Xej selected from the time intervals r,; J’ = 1 , - *. , ne; (by definition El, = T,)

ni = number of events in the i-th complete

nc

(X>

X max

G.A. PAPADOFOULOS AND A. KIJKO

subcatalog with magnitudes Xi, 2 mj, i=f ‘.‘., s; j = 1,. . . , n,

= number of events in the complete part of catalog; (by definition Ez, = n,)

= mean earthquake magnitude determined from the extreme and complete parts of catalog

= largest observed magnitude in the whole catalog.

Assuming that the earthquake process is Pois-

sonian and taking into account the doubly trun- cated G-R dist~bution, we get the fo~o~g equations through the maximum likelihood method (Kijko and Sellevoll, 1987; 1989):

l/X, = cpl” + ta; (1)

l/~=(x)-Q1~+~,f+xO(cp~+Qh,c) (2)

where:

*): = roB,

i=l

i=l

Moreover, we have: s

n= Cn, I=0

r, = ni/n

A, = exp( - Bmo)

A2 = exp( - Pmmax )

A(m) =exp(-Pm)

4 = f WAz - (tA))/( A, - A,)

4 = (O&A) - Wm,,A,V(A, -A,)

ci=l-F(mj)

4 = E(mov mi) - Etm,, m~~~)~(mi)

where i = 1,. . . , s. In addition:

E(x, Y) = [xA(x) -y~f~k’[A~~) -A,]

F(x) = [A, - A(x)],&% -A,]

ESTIMATION OF GsRTHQUAKE HAZARD PARAMETERS IN THE AEGEAN

and:

where the summation is from i = I,. . . ) n,.

The indices E and C are introduced in order to distinguish different sources of functions @. If they are derived from the extreme part of catalog, they are marked as E. Otherwise they follow from the complete parts (subcatalogs) and are marked

as C. Introducing the condition that the largest ob-

served magnitude, X,,,,,, is equal to the largest expected magnitude in the span of the whole

catalog, T, we get:

X max = EXPECTED{ x,,, 1 Ii’>

where (Kijko, 1988):

EXPECTEDC xmax \ T)

Jw-z2) - E;W,) = mmax -

B exp( - TZ,l

- m, exp( - h,T)

(3)

In eqn. (3) Z, =AA,, 2, =hA2, x = &,/(A, -

A,) and E,(.) denotes an exponential integral function. By introducing the condition (3) into relations (1) and f2), we obtain a set of equations determining the maximum likelihood solution, which can be solved by iteration.

Figure 1 illustrates the variable quality of data

which can be used to obtain seismic hazard

parameters applying the procedure of Kijko and

279

Sellevoll (1987, 1989). The approach permits the combination of the largest historical earthquakes reported, which occurred before the start date of the complete part of the catalog, with the complete data contained in the subcatalogs and defined by variable magnitude thresholds. It also accepts “gaps”, that is, time intervals during which records are missed or seismic networks were not in

operation. The seismic hazard parameters dete~ned in

this paper are b (or, equivalently, the slope of G-R relation b), i4,5, J&,,,,, and R for several values of m.

Earthquake files and computational remarks

Several earthquake catalogs for the Aegean and surrounding regions have been published (see short reviews in B&h, 1983; Makropoulos and Burton, 1985). For the historical (pre-19~) period, the most recent, complete and homogeneous catalog for strong earthqu~es is that of Pap~chos and Comninakis (1982). To ensure that all the seismological information used in this paper is as homogeneous as possible, we used the catalog produced by the same authors for the instrumental period (Comninakis and Papazachos, 1986). The time interval covered by these two earthquake catalogs is 479 B.C.-1985 A.D. Only main shocks were

I+---- only extremes + compiete parts ot catalog I

I-- SPAN OF THE CATALOG ~

-___..

Fig. 1. An illustration of the data which can be used to obtain basic seismic hazard parameters by the procedure proposed (Kijko and Sellevoll, 1987, 1989). Our approach permits combination of the largest earthquakes with complete data having variable threshold magnitudes. It makes it possible to use the largest known historical earthquake (X_) which occurred before the beginning of the

catalog. It also accepts “gaps” (as Ts) when records are missing or seismic networks were not in operation.

280 G.A. PAPADOPOULOS AND A. KIJKO

considered. ~on~quently, the results of the seismic

hazard determination concern background seismic

activity from main shocks,

The plot of earthquake magnitude versus frequency or other statistical tests which have been used by various authors, indicate that the completeness of our earthqu~e data is different for different time intervals. Before 1800 A.D. it

seems impossible to define a ma~itude level above which the data can be considered as complete.

Thus, the pre-1800 period constitutes the extreme

part of our whole catalog (covering the time interval from 479 B.C. to 1799 A.D.). For c~nve~en~e we changed 479 B.C. to 500 B.C., so that T = 2486 y. The remai~ng material, from the interval 1800-1985 is the complete part of the catalog.

Fig. 2. The eighteen seismotectonic segments of the Aegean area (after Papazachos, 1980) and their relative hazard level. Stipple = areas of low seismic hazard (K = 2); vertical ruling = intermediate hazard (K = 3); horizontal ruling = high hazard (K = 4);

cross-hatching = areas of very high seismic hazard ( K = 5).

ESTIMATION OF EARTHQUAKE HAZARD PARAMETERS IN THE AEGEAN 281

TABLE 1

Earthquake subcatalogs defined for the period 1800-1985 on

the basis of the magnitude threshold, mi. Also @en is the time

interval 7; for which the data are complete

Subcataiog

i=l (C) 1800-1910 6.5

=l (I) 1800-1910 6.9

= 2 (C, I) 1911-1949 5.2

= 3 (C, I) 1950-1963 4.8

= 4 (C, I) 1964-1985 4.5

C = crustal shocks; I = intermediate depth shocks.

This has been divided into subcatalogs (s = 4),

with different magnitude thresholds as indicated

in Table 1. It is obvious that T, = 186 y.

It was assumed that for all cases, the maximum

observed magnitude X,,,,, was determined with

standard error, ox, equal to l/4. The approximate

standard deviation of km,, is (Kijko and Selle-

~011, 1987, 1989):

IJ msx = rux

where r is a “transmission coefficient” which

transmits the uncertainties in X,,, into the uncer-

tainties of #._,.

The Aegean region is highly complicated from

seismotectonic point of view (e.g. Papadopoulos et

al., 1986) and for this reason we evaluated seismic

hazard parameters for several seismotectonic seg-

ments. Based on several criteria such as fault

plane solutions, seismicity rates, etc., Papazachos

(1980), divided the whole region into nineteen

distinct seismotectonic segments. The nineteenth

segment, however, located in northern Greece,

seems to be only a part of the shallow seismic

activity occurring even more to the north in the

area of Bulgaria. Therefore, this segment has not

been considered here. Figure 2 shows the eighteen

segments for which hazard parameters have been

estimated.

The first five segments (l-5) constitute the

outer or fore-arc seismic zone while the remaining

segments (6-18) form the inner or back-arc seismic

zone. Seismic hazard parameters are also esti-

mated for these two zones and the area as a whole

(l-18), as well as for intermediate depth earth-

quakes (IDE) (h 2 70 km) occurring in the South

Aegean as a result of the active subduction of the

Mediterranean lithosphere.

One problem we faced in applying the method

summarized earlier is the small number of events

in the extreme part of the catalog. In the cases

where there were only a few events in a long time

span (the extreme part of the catalog), and many

events in a complete subcatalog, that is, in a short

time span, the inversion procedure is very sensitive

and strongly disturbed, resulting in meaningless

parameter estimation. Consequently, if, for a

specified segment, the extreme part of catalog

contained no more than four events (n, c 5) we

omitted them from the computations. The method

of kI-&Z. evaluation was performed using the largest

earthquake, X,,, , that ever occurred in the entire

TABLE 2

Description of the input data used for seismic hazard evahra-

tion in the Aegean and surrounding regions

Segment T, “e T, “c X max

1 2300 10 186 144 6.9

2 2300 22 186 116 7.3

3 0 0 186 85 7.5

4 2300 7 186 191 7.1

5 0 0 186 116 7.2

6 0 0 76 40 6.9

7 0 0 76 30 7.0

8 2300 8 186 65 7.3

9 2300 8 76 54 7.5

10 2300 6 76 33 7.0

11 0 0 186 16 7.1

12 0 0 186 28 7.1

13 2300 9 186 51 7.1

14 0 0 186 41 7.2

15 0 0 76 36 7.1

16 2300 25 186 30 7.8

17 23M1 6 186 21 7.0

18 0 0 186 25 7.8

l- 5 2300 43 186 652 7.5

6-18 2300 72 186 470 7.8

l-18 2300 11.5 186 1122 7.8

IDEE 2300 4 186 164 8.3

IDEC 0 0 186 164 8.3

T,. T,, T, n,, n,, and X,,,,, are explained in the text. T = 2486

y for ail segments. X,, is expressed in surface-wave magni-

tude, M. IDEE = intermediate depth earthquakes from both

the extreme and complete parts of the cataiog; IDEC = IDE

from only the complete part of the catalog. The segments are

shown in Fig. 2.

282 G.A. PAPADOPOULOS AND A. KIJKQ

TABLE 3

Information contributed by the complete parts of the catalog in the determination of the hazard parameters

Segment i=l i=2 i=3

6 IW .x PI a l%l x WI p^ I%1

I 5.8 6.5 12.0 20.8 0.9 2 11.2 6.5 6.0 18.8 2.8

3 24.9 5.9 30.3 8.3 14.5 4 7.1 1.0 17.9 15.2 6.8

5 17.1 2.6 33.2 13.8 10.3 6 45.8 22.5 10.9

7 _ 47.9 23.3 19.8 8 8.3 9.6 5.2 17.8 0.7

9 _ 9.8 16.2 3.6 10 9.3 10.4 3.5

11 26.9 6.3 36.6 31.3 7.6 12 36.3 14.2 22.6 17.9 9.9

13 6.7 10.0 8.7 6.7 2.7

14 33.4 9.8 25.8 12.2 9.6 15 _ _ 45.0 19.4 17.3 16 6.8 5.5 2.8 5.5 0.3

17 11.2 14.8 3.2 3.7 2.5 18 43.8 12.0 20.1 28.0 5.5 l- 5 6.5 7.0 12.0 15.6 4.5 6-18 7.4 6.1 5.1 14.7 1.1 1-18 7.1 5.1 6.8 15.6 1.5

IDEE 3.7 5.3 6.6 22.9 1.3

IDEC 31.7 5.5 26.8 23.8 8.3

The number of each subcatalog, i, refers to Table 1. IDEE and IDEC as in Table 2.

i=4

fi l%l B 1st A PI

6.5 15.2 59.7

16.7 12.0 42.0

21.2 30.2 64.7

16.2 16.3 64.5

13.8 39.4 69.8

10.0 43.3 67.5

23.3 32.3 53.4

11.0 11.3 50.7

14.6 8.1 56.8

12.9 7.9 62.0

12.5 28.9 49.9

17.9 31.2 50.0

8.4 9.7 60.2

14.6 31.3 63.4

19.4 37.7 61.1

7.3 10.8 36.4

14.8 16.8 44.4

12.0 30.0 48.0

13.9 10.3 57.9 12.7 11.3 53.2

12.6 12.3 57.4

14.1 10.3 54.1

14.6 33.2 56.1

interval, T. If &,,,, takes the value of X,,,, we

finally obtain k,,,,, = X,,, + 0.1.

Seismic hazard parameters for the segments 1,

2, 4, 8, 9, 10, 13, 16, 17, l-5, 6-18, and 1-18 were

calculated utilizing both the complete and extreme

parts of the catalog. Only complete data (four

complete subcatalogs) were used to estimate

hazard parameters for the segments 3, 5, 6, 7, 11,

12, 14, 15, and 18.

The number of reported intermediate depth

earthquakes which occurred before 1800 is ne = 4

< 5. In this case we made two alternative calcula-

tions; one using only the complete part of the

catalog and another using both extreme and com-

plete data. The results obtained by both calcula-

tions are given in order to point out the dis-

crepancy between them.

Table 2 summarizes the input data used for the

seismic hazard estimation in the Aegean seismo-

tectonic segments, while Table 3 shows the per-

centage of information contributed from the four

complete subcatalogs in the determination of the

hazard parameters.

Results

The values obtained of the parameter 6 are

shown in Table 4. The slope b’ of the G-R

relation determined by other authors by the least-

squares method is also given for comparison. Ta-

ble 5 provides the estimated values of seismic

hazard parameters &,,,,, fi,.,, and R for several

levels of FK Figure 3 illustrates the mean return

periods and probability that a certain magnitude

will not be exceeded in any year for the segments

examined.

From Table 5 it follows that the maximum

possible earthquake magnitude, e,,,,,, varies sig-

nificantly from segment to segment. On a regional


RETURN PERIOD (YEARS)

7.5

!iY 7.0

3 I- ; 6.5

0 e I 6.0 SEGMENT

5.5

.O 9

PROBABI LlTY


-

!_ SEGMENT

2

- $1) r IIk I -__ i .OOl .Ol .05 S .2 .3 .4 .S .6 .7 .?5.0 .85 .9 .95 .99 ,995 .999

PROBABILITY


1.5 2 3 4 5 10 20 50 100 500

7.5

ii 7.0

3

k 6.5 N z c1 0’

C ; 6.0 I/

,“I

SEGMENT

5.5 3

.OOl .Ol .06 .1 .2 .3 .4 .5 .6 .7 35.9 .85 .9 .95 .QQ .QQ5 ,999

PROBABILITY

Fig. 3. The mean return pe~~/probab~ty/ma~tude diagram for each segment shown in Fig. 2.



1.1 1.5 2 3 45 10 20 50 100 500

.OOl .OI .05 .l .2 .3 .4 .5 6 7.75.8 .85 .9 .95 .99 ,995 ,999

PROBABILITY


1.1 1.5 2 3 45 10 20 50 100 500 8.0

7.5

7.0

6.5

6.0 ,I

YE

SEGMENT

5.5 ,' II 4' 5

-l I .OOl .Ol .05 .l .2 .3 .4 .5 .6 .7.75.6 .B5 .9 .95 .99 ,995 .999

PROBABILITY


1.1 1.5 2 3 45 10 20 50 100 500

7.5

p" 7.0 3 5 6.5

z : 6.0 SEGMENT

5.5

.oOl .Ol .05 .l .2 .3 .4 .5 .6 .7.?5.8 .85 .9 .95 .99 .9% ,999

PROBABI LITV

Fig. 3 (continued).

ESTIMATION OF ELARTHQUAKE HAZARD PARAMETERS IN THE AEGEAN 285


6.5

6.0 ,’

I SEGMENT

5.5 40 I’

7

-r 1 .CQl .Ol 05 1 .2 .3 .4 .5 .6 .7 75.0 .Q5 .Q .95 .QQ 9% .QQQ

0.0

7.5

7.0

6.5

6.0

5.5

PROBABILITY


SEGMENT

+ .OOl .Ol 05 .l .2 .3 .4 .5 .6 .7.75.8 85 .Q .95 .QQ .s

PROBABILITY


0.0

7.5

7.0

6.5

6.0 SEGMENT

5.5

.OOl .Ol .05 .l .2 .3 .4 .5 .6 .7 75.8 .85 .Q .95 .QQ ,995 ,999

PROBABILITY

Fig. 3 (continued).



7.5

: 7.0 1 I- I In

; 6.5

0 4 z! 6.0 SEGMENT

5.5 I/

/’

1 10

1' I

-I I 001 .Ol 05 .l .2 3 .4 .5 .6 .7.75.9 .85 .9 .95 .99 ,995 ,999

PROBABILITY


1.1 1.5 2 3 4 5 10 20 50 100 500 8.0

7.5

ii 7.0 3 I- z 6.5

u ii 6.0 SEGMENT

5.5

,001 .Ol .05 .l .2 3 .4 .5 .6 .7.75.0 .95 .9 .95 .99 ,996 .999

PROBABILITY

RETURN PERIOD (VEARS)

8.0

7.5

7.0

6.5

6.0

5.5

1.1 1.5 2 3 45 10 20 50 100 500

I I II IIIII III1

/ 0’ L

/ SEGMENT

.oOl .Ol .05 .l .2 .3 .4 .5 .6 .7.75.9 .85 .9 .95 .99 .QQ5 .999

PROBABILITY

Fig. 3 (continued).

ESTIh4ATION OF EARTHQUAKE HAZARD PARAMETERS IN THE AEGEAN 287


z 0 4

B

6.5

6.0 SEGMENT

5.5

PROBABILITY


1.1 1.5 2 3 45 10 20 50 100 500 9.0

7.5

7.0

6.5

6.0

5.5

0.0

7.5

7.0

6.5

6.0

5.5

PROBABILITY


1.1 1.5 2 3 45 10 20 50 100 500

SEGMENT

.CQl .Ol .05 .l .2 .3 .4 .5 .6 .7.75.0 .95 .9 .95 .99 .995 .999

PROBABILITY

Fig. 3 (continued).


0.0

7.5

7.0

6.5

6.0


SEGMENT

.OOl .Ol .05 .I .2 .3 .4 .5 .6 .7.75.8 .85 .Q .95 .QQ .QQ5 ,999

PROBABILITY


6.0 SEGMENT

5.5

,001 .Ol .05 .I .2 .3 .4 .5 .6 .7 ,758 .85 .Q .95 .QQ .QQ5 .9

PROBABILITY


1.1 1.5 2 3 45 10 20 50 100 500 __ u,cl

7.5

7.0

6.5

6.0

5.5

SEGMENT

.OOl .Ol .05 .l .2 .3 .4 .5 .6 .7 .75.8 .05 .Q .95 .QQ .Q% .QbQ

PROBABILITY

Fig. 3 (continued).

ESTIMATION OF EARTHQUAKE HAZARD PARAMETERS IN THE AEGEAN


0.0

7.5

7.0

6.5

/' I' S

6.0

0’

SEGMENT

5.5 / d' l-5

-I 1 I .OOl .Ol .05 .l .2 .3 .4 .5 .6 .7.75.0 .65 .9 .95 .99 .995

PROBABILITY


1.1 I.5 2 3 45 10 20 50 100 500 8.0

7.5

7.0

6.5

6.0 SEGMENT

5.5

.OQl .Ol .05 .l .2 .3 .4 .5 .6 .7.75.0 .65 .9 .95 .99 ,995 .S

PROBABILITY


1.1 1.5 2 345 10 20 50 100 500 . .

0.0

7.5

7.0

6.5

6.0

5.5

I4 /-

U AN

I- SEGMENT

I’ -I 1-18

1 I I

289

DO1 .Ol .05 1 .2 .3 .i .5 .6 .7.75.0 .es .9 .95 .99 995 .999

PROBABILITY

Fig. 3 (continued).

290 G.A. PAPADOPOULOS A


.ND A. KIJKO

8.0

6.0 SEGMENT

5.5

! !KiiI!ii!!! .OOt .Ol .05 S .2 .3 .4 5 .6 .7.75.8 .85 .9 ‘95 .QQ .QQ5 .99Q

PROBABILITY

RETURN PERI~~I (YEARS)

- 1.1 1.5 2 3 4 5 10 20 50 100 SOO--

8.0

7.5

7.0

6.5

6.0 SEGMENT

5.5

PROBABILITY

Fig. 3 (continued).

scale, tim, = 7.90. However, &,,,, is only equal to 7.53 in the fore-arc zone (segments l-5) while it is larger (&, = 7.90), in the back-arc region (segments 6-18).

On a local scale strong differences are observed in the spatial distribution of gm,. For example, segment f7, with &,,= = 7.04, is located between the segments 16 and 18 with &,._ = 7.89 and 7.75, respectively. However, cimax seems to be almost stable in the central Aegean area where its value varies between 7.14 and 7.26 in segments 10-15. The largest values of @,,, appear in the back-arc segments 9 (Gmm = 8.33), 16 (kmaX = 7.891, and 18 (h?,,,, = 7.75); the smallest values

(&?,X = 7) are present in the northwest section of the region (segments 1 and 6), that is, in northwest Greece and Albania. In the major part of the

fore-arc zone (segments 2-5) E;j,,, is relatively low, varying between 7.13 and 7.62. Of interest is the high standard deviation (= 1.64) for the &,,, of segment 9.

The j’&, obtained for intermediate depth earthquakes is 8.41, using the extreme part of catalog, and 8.35, using only the complete data, with standard errors of 1.28 and 0.54, respectively. As we will explain later the second solution is considered to be more reliable.

The return period, R, of earthquakes with a magnitude equal to or larger than a certain value, m, is a useful parameter in seismic hazard determination. Table 5 provides values of R for several m values starting from m = 5.0, and the activity rate X4.5. It is important to point out that x4,5 of the fore-arc segments is significantly higher


TABLE 4

Values of parameter b and their standard deviations &,, ob-

tained in our study

Segment b eb b’

1 1.25 0.06 1.01

2 0.86 0.06 0.86

3 1.04 0.09 0.84

4 1.14 0.05 1.14

5 1.22 0.09 1.02

6 0.89 0.13 0.84

7 1 .Ol 0.16 1.08

8 1.03 0.07 1.14

9 1.22 0.07 0.70

10 1.13 0.09 0.59

11 0.98 0.22 0.87

12 0.79 0.15 0.64

13 1.07 0.07 0.87

14 0.78 0.10 0.59

15 0.98 0.14 0.61

16 0.73 0.17 0.46

17 0.72 0.07 0.78

18 0.61 0.13 0.51

l- 5 1.15 0.02 1.06

6-18 1.07 0.03 0.95

1-18 1.14 0.02 1.06

IDEE 1.14 0.05 0.68

IDEC 0.78 0.05 0.68

b’ is the same parameter determined by the least-squares

method by Papazachos (1980) for the segments l,.. .,18;

Papadopoulos (1982) for 1-5, 6-18 and l-18, and Papado-

poulos (1989) for IDEE and IDEC. IDEE and IDEC as in

Table 2.

than that of the back-arc segments. This is also

indicated by the A,, values for the segments l-5

and 6-18. For m 2 6.0, however, the return peri-

ods in segment l-5 are higher than the periods in

segment 6-18, implying that strong events (M 2

6.0) occur more frequently in the inner seismic

zone than in the outer zone. Papadopoulos (1982)

observed this difference in magnitude-frequency

relationships, determined using the least-squares

method, in 1911-1978 data. Considering the val-

ues of R,,,, R,.,, and R,, one may argue that

segment 2 in the Ionian Islands is the most active

in the region. Very active also are segments 16 and

18 in the Marmara Sea and Serbomacedonian

geological zone, respectively. To group all the 18

segments in classes based on their level of seismic

hazard we took into account equally their &?,,,aX

and R,,. We suggest that the seismic hazard is a

function of the form 8( M,,, R,,,) increasing with

M max and decreasing with R,,. For M,,,,, < 7.2,

7.2 I M,,,,, < 7.6, and M,,, 2 7.6, we define

e(M,,,,,) equal to 2, 4, and 6, respectively. We

define fl( R,,,) equal to 2, 4, and 6 for R,, 2 30,

30 > R,,, 2 17.5, and R,, -c 17.5, respectively. The

arithmetic mean K = +[a( M,,,,,) + 0( R6,0)] sig-

nifies the adopted relative seismic hazard of a

specific segment. K takes the values 2, 3, 4, and 5

leading to the definition of four classes of relative

seismic hazard: low (K = 2) intermediate (K = 3),

high (K = 4) and very high (K = 5).

Figure 2 shows how the segments are classified

in the relative seismic hazard scale. This classifica-

tion does not change drastically if we change

either the intervals of M,,, and R,,, ranked by 2,

4 or 6, or the value of m by using, for example,

R,,5 instead of R,,,.

Although the values of fi,, obtained for the

two alternative calculations concerning inter-

mediate depth shocks are almost identical, the

return periods, R, for magnitude levels of m 2 5.0

deviate significantly. Where the extreme part of

the catalog has been considered (IDEE in Table

5), R is much higher than the value obtained for

the same m value using only the complete part

(IDEC in Table 5). Thus, the R,., of IDEE ex-

ceeds the R,., of IDEC by a factor of 7. We

believe that the IDEE results are totally non-

realistic because of the small number of events

(n, = 4) in the extreme part of catalog. Values of

R (m I 7) for IDEC are compatible with return

periods determined by Papadopoulos (1989) using

the least-squares method on 1800-1985 data. For

m > 7, however, there is some deviation.

The parameter b of the G-R relation is one of

the most important parameters in seismology.

Apart from its importance in seismicity and earth-

quake prediction studies, b is an indicator of the

mechanical properties in the seismogenic material,

such as stress concentration, crack density and

degree of heterogeneity. Table 4 shows that on a

regional scale the 6 value is relatively high (about

1.1 for the region as an entity, as well as for

fore-arc and back-arc regions) expressing the high

fracturing, locally concentrated stresses, and high

degree of heterogeneity. The 6 value exhibits

292 G.A. PAPAWF’OULOS AND A. KIJKO

TABLE 5

Results of k,,,=, A.,, and R determination

Segment ‘k, * c, fi,* * 6, (events/y)

Return periods R (y)

m = 5.0 M = 5.5 M = 6.0 m = 6.5 m = 7.0

1 7.00 0.56 4.1 0.4 1.0 4.4 19.2 100

2 7.40 0.26 2.8 0.3 1.0 2.7 7.5 23

3 7.62 0.32 2.3 0.3 1.5 5.0 17.5 63

4 7.13 0.27 5.3 0.4 0.7 2.8 11.3 51

5 7.30 0.42 3.4 0.3 1.2 4.9 20.3 90

6 6.93 0.26 1.0 0.2 2.8 8.1 25.6 105

J 7.08 0.30 0.8 0.2 4.0 13.3 46.3 188

8 7.35 0.66 1.6 0.2 2.1 6.8 22.7 82

9 8.33 1.64 1.5 0.2 2.8 11.6 47.6 205

10 7.15 0.36 0.9 0.2 4.2 16.5 66.1 295

11 7.26 0.70 0.4 0.1 7.4 23.2 74.8 266

12 7.14 0.54 0.6 0.3 3.8 9.8 26.4 83

13 7.18 0.30 1.4 0.2 2.6 9.2 33.9 138

14 7.23 0.26 1.0 0.2 2.6 6.8 18.2 55

15 7.17 0.29 1.0 0.2 3.2 10.4 34.7 130

16 7.89 0.58 0.7 0.3 3.3 7.8 18.7 46

17 7.04 0.56 0.4 0.1 6.1 14.6 37.5 119

18 7.75 0.54 0.5 0.1 4.1 8.5 18.0 40

l- 5 7.53 0.27 17.6 0.8 0.2 0.9 3.4 14

6-18 7.90 0.56 12.3 0.7 0.3 1.0 3.3 12

l-18 7.90 0.54 30.0 1.0 0.1 0.5 1.7 J

IDEE 8.41 1.28 4.0 0.4 0.9 3.4 12.8 48

IDEC 8.35 0.54 3.8 0.3 0.6 1.6 3.9 10

99

256

536

575

2665

410

866

2831

1520

692

1101

297

1002

125

2510

103

66

44

26

183

25

%m% and M are expressed in surface-wave magnitude, M. G,,,, and 8, are the standard deviations of M,, and A,,, respectively.

IDEE and IDEC as in Table 2.

strong differences from one segment to another. Relatively high 5 values characterize all the fore- arc segments.

Comparison with values determined using the least-squares method by other authors (see b’ in Table 4) indicates that 6 values are as a rule higher than b’ values (Fig. 4). This is probably due to the fact that b’ values were determined from data covering only part of the instrumental era, which means that in most segments the relative number of events of magnitudes having long return periods are extremely low. It is characteris- tic that in segments that have strong events with

short return periods;of, for example, A4 2 6.5 (see Table 5), the values of 5 and b’are either identical (segments 2 and 4) or do not deviate significantly (segments 3, 18, l-5, 6-18, 1-18). The same is

Fig. 4. Comparison of b values determined using the methods

described in this paper (6) with values determined using the

least-squares method (b’) (see Table 4).


valid for the segment IDEC (B = 0.78) where the

b’ = 0.68 value has been calculated from data

covering the 18OC-1985 time interval (Papado-

poulos 1989). In contrast, the 6 of IDEE (1.14)

deviates significantly from b’, implying, once

more, how unsuitable the use of the extreme part,

with a small number of events, is.

The largest differences between 6 and b’ val-

ues appear in segments 9,10, and 15. In segment 9

only two events, of M = 6.6 and 7.5, took place

during the interval (1919-1978) used by Papa-

zachos (1980) for the b’ value determination. On

the other hand, four events of M 2 6.5 are re-

ported in the pre-1919 interval. In segment 10 the

b’ value is determined from 1911-1978 data. Two

events of M 2 6.5 occurred during this time, while

three events of M 2 6.5 are reported in the pre-

1911 period and one more strong shock of M = 6.5

took place in 1980. In segment 15 the b’ value has

been determined from data covering the interval

1916-1978, during which two events of Ma 6.5

were recorded. One event of M = 6.5 is reported

in the pre-1916 period.

Summary and discussion

The reliability of results for seismic hazard

estimation in a given region depends on the meth-

odology and information input used. Here we

have applied a procedure utilizing both instrumen-

tal and historical seismological information cover-

ing many hundreds of years. Although the proce-

dure is purely stochastic, the base of our method-

ology is geophysical since we consider several data

sets corresponding to several segments defined by

certain seismotectonic features. As a consequence,

the hazard of each segment is independently de-

termined.

The same stochastic procedure was applied in

23 different data sets, thus giving the opportunity

for methodological tests. From this point of view

it is noteworthy that the results obtained seem to

be realistic. The example of the intermediate

depth earthquakes indicates how unsuitable the

use of the extreme part of the catalog is when only

a small number of events are considered. This is

the reason why in some segments the hazard

estimation has been based solely on the complete

part of the catalog.

To quantify the differences in the hazard level

from segment to segment we suggested that the

seismic hazard increases with M,,, and decreases

with R. A relative hazard scale is defined and a

factor K is calculated for each segment. This is

used to classify the segments in to one of four

hazard classes: low, intermediate, high, very high,

corresponding to values of K equal to 2, 3, 4, and

5, respectively.

A general conclusion is that the seismic hazard

is sharply higher in the back-arc zone (segments

6-18) than in the fore-arc zone (segments 1-5)

(Table 5). However, the strongest differences in

the distribution of K (that is, the hazard level), are

found in the back-arc zone (Fig. 2) where the

stress field and seismotectonics are complicated

(Papadopoulos et al., 1986). In contrast, the fore-

arc zone, including the segment 6, is seismotecton-

ically more homogeneous, which is consistent with

the relatively smoothed distribution of the factor

K. The same is also valid for the b value distribu-

tion (Table 4).

The distribution of hazard levels from segment

to segment is informative and useful not only

from a theoretical but also from a practical point

of view. Its theoretical importance is that the

strong differences in K value, even between ad-

jacent segments, is a direct reflection of the high

seismotectonic complexity and inhomogeneity in

the Aegean area. The relative hazard classification

is useful for engineering or other practical pur-

poses, allowing the designation of priority areas

for earthquake-resistant design.

Acknowledgements

We are grateful to Professor M.

Sweden) for reviewing the paper.

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Maximum likelihood estimation of earthquake hazard parameters in the Aegean area from mixed data

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